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In triangle PQR, let M be the midpoint of QR, let N be the midpoint of PR, and let O be the intersection of QN and RM, as shown.  If QN perp PR, QN = 12, and PR = 14, then find the area of triangle PQR.

 

 Nov 29, 2022
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Im very confused. You say it is a triangle, but it is not. Do you mean connecting Q and R to form a triangle? But then the answer would be pretty straight forward. \(\frac{12*14}{2}\) which will be 84. But i assume you mean the area of the figure shown here. So i will solve that too

 

Here is what i hope to be the solution: 

First lets find \(\overline{PQN}\) which will be 42 (use the triangle calculation formula \(\frac{base*height}{2}\))

Heres where things get trickier, but I want you to figure it out, but i will give you some hints

1. draw a line from P to the midpoint of \(\overline{QR}\)

2. try to see if you can combine triangles in some way to single out \(\overline{NOR}\) to find it

 Nov 29, 2022

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